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I am looking for Sperner-type lemmas where:

  • The colors are on the edges (1-dimensional simplices) - rather than on the vertices;
  • The target is a fully-colored vertex (a vertex adjacent to n edges of different colors) - rather than a fully-colored simplex.

What are some lemmas of this type?

Alternatively: is there a way to derive such a lemma from known lemmas, e.g. using some "dual" construct mapping edges to vertices and vertices to simplices?

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